Practice problems of the right triangle - page 59 of 81
A right triangle is a type of triangle that has one angle that measures exactly 90 degrees (a right angle). This angle is formed by the intersection of two of the triangle's sides, which are called the legs of the triangle. The other side of the triangle is called the hypotenuse, which is the side opposite the right angle, and is the longest side of the triangle. Right triangles are important in mathematics and are used in many areas of science and engineering, including trigonometry, physics, and construction. The Pythagorean theorem which states that in a right triangle, the sum of the squares of the legs (a,b) equals the square of the hypotenuse (c) is a fundamental result in geometry.Number of problems found: 1619
- Laths
There are two laths in the garage opposite one another: one 2 meters long and the other 3 meters long. They fall against each other and lean against the opposite walls of the garage. Both laths touch at 70 cm above the garage floor. How wide is the garage - Dig water well
Mr. Zeman is digging a well. Its diameter is 120 cm and plans to be 3.5 meters deep. How long (at least) must be a ladder, after which Mr. Zeman would have eventually come out? - Perpendicular 32733
Calculate the right triangle ABC, the perpendicular b = 43.5 cm of the hypotenuse c = 72.9 cm. Calculate: A hypotenuse segment cb, side a, a hypotenuse segment ca, and a height of triangle v - Water channel
The cross-section of the water channel is a trapezoid. The bottom width is 19.7 m, the water surface width is 28.5 m, and the side walls have a slope of 67°30' and 61°15'. Calculate how much water flows through the channel in 5 minutes if the water flows - The ditch
Ditch with a cross-section of an isosceles trapezoid with bases 2m and 6m deep 1.5m. How long is the slope of the ditch? - Cap
A rotating cone shapes a jesters hat. Calculate how much paper is needed for the cap 54 cm high when the head circumference is 47 cm. - Circumference 4956
Calculate the circumference of a diamond whose area is 288cm square and one diagonal is 12.4cm. - Diagonals of rhombus
Find the length of the diagonal AC of the rhombus ABCD if its perimeter P = 112 dm and the second diagonal BD has a length of 36 dm. - Leg
Determine the trapezoid area with bases 32 and 12; the height is 2 shorter than its leg. - The quadrilateral
The quadrilateral ABCD is composed of two right triangles, ABD and BCD. For side lengths: |AD| = 3cm, | BC | = 12cm, | BD | = 5cm. How many square centimeters (area) does the quadrilateral ABCD have? The angles of DAB and DBC are right. - Mass point
Two equal forces of 30 Newtons act on a mass point. Find the magnitude of the resultant force if these forces form an angle of 42°. - Determine 82341
Determine the equation of the circle that is the set of all points of the plane that are twice as far from the point [3,7] as they are from the point [0,1]. - Triangle IRT
An isosceles right triangle ABC with right angle at vertex C has vertex coordinates: A (-1, 2); C (-5, -2). Calculate the length of segment AB. - The trapezium
The trapezium is formed by cutting the top of the right-angled isosceles triangle. The trapezium base is 10 cm, and the top is 5 cm. Find the area of the trapezium. - Diamond diagonals
Find the diamond diagonal's lengths if the area is 156 cm² and the side is 13 cm long. - Diamond diagonals
Calculate the diamonds' diagonal lengths if the diamond area is 156 cm square and the side length is 13 cm. - The pyramid 4s
The pyramid with a rectangular base measuring 6 dm and 8 dm has a side edge of a length of 13 dm. Calculate the surface area and volume of this pyramid. - Triangular prism
Calculate the surface area and volume of a three-sided prism with a base of a right-angled triangle, if its sides are a=3cm, b=4cm, c=5cm and the height of the prism is v=12cm. - Diagonal
Determine the dimensions of the cuboid if diagonal long 60 dm has an angle with one edge 35° and with another edge 77°. - Estate
An estate-shaped rectangular trapezoid has bases long 35 m, 65 m, and perpendicular arm 34 m. Calculate how long its fence is.
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